拼接误差可控的扫掠曲面生成算法  

SWEEP SURFACE GENERATION ALGORITHM WITH CONTROLLABLE SPLICING ERROR

作　　者：王帅 刘浩 刘秀平[1] 吴梦 Wang Shuai;Liu Hao;Liu Xiuping;Wu Meng(School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China;Hefei Jiushao Intelligent Technology Co.,Ltd.,Hefei 230022,China;School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]大连理工大学数学科学学院,大连116024 [2]合肥九韶智能科技有限公司,合肥230022 [3]南京理工大学数学与统计学院,南京210094

出　　处：《数值计算与计算机应用》2025年第1期3-23,共21页Journal on Numerical Methods and Computer Applications

摘　　要：扫掠曲面生成是计算机辅助几何设计(Computer-Aided Design,CAD)领域中的关键技术,在工程设计等领域有着广泛应用.针对此问题,本文首先给出了与给定B样条曲面几何拼接的单轨和双轨扫掠基础算法,然后提出了一种拼接误差可控的扫掠曲面生成算法,随后将这些算法生成的曲面与商业软件Catia和Rhino得到的结果进行了对比分析.在本文拼接误差可控的扫掠曲面生成算法中,首先对给定曲面边界进行采样,获取导数和参数等信息,然后对这些信息进行B样条曲线插值.通过该B样条曲线进行扫掠操作以获得扫掠曲面.最后根据预设的扫掠曲面与给定曲面之间的拼接误差阈值,对采样点进行调整,以获得拼接误差范围内的扫掠曲面.实验结果表明,本文中的算法在生成曲面质量方面优于Rhino,并且能以较少的控制点数量生成与Catia质量相当的曲面.Sweep surface generation is a key technique in the field of Computer-Aided Design(CAD),widely used in engineering design and other fields.To address this problem,this paper first presents the basic single-rail and dual-rail sweep algorithms for geometric splicing with a given B-spline surface,and then proposes a swept surface generation algorithm with controllable splicing errors.Subsequently,the surfaces generated by these algorithms are compared and analyzed with the results obtained by the commercial software Catia and Rhino.In the swept surface generation algorithm with controllable splicing error in this article,the boundary of the given surface is first sampled to obtain information such as derivatives and parameters,and then B-spline curve interpolation is performed on this information.Perform a sweep operation through this B-spline curve to obtain a swept surface.Finally,based on a preset threshold for splicing errors between the sweep surface and the given surface,the sampling points are adjusted to obtain a sweep surface within the acceptable error range.Experimental results show that the algorithm in this article is better than Rhino in generating surface quality,and can generate surfaces with a quality comparable to Catia with a smaller number of control points.

关 键 词：扫掠曲面 B样条曲面 几何拼接 误差阈值 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]